Abstractions for Modeling the Effects of Wall Surface Roughness in Silicon Photonic Microring Resonators

Microring resonators (MRRs) are one of the key components of many on-chip optical interconnect wavelength-division multiplexing (WDM) network architectures, often fab-ricated in Silicon Photonics. The operation of these devices is extremely sensitive to variations in the fabrication process. Wall surface roughness (WSR) is one such process variation that affects MRR's performance. Analyzing the effect of WSR on MRR's performance requires full-scale FDTD simulations, which is costly for testing and validation of silicon photonic circuits. This paper proposes an abstract mathematical model to estimate the impact of WSR on the shift in the resonant wavelength of MRRs. We show that WSR can be approximated using a quasi-grating - in particular, a “notch perturbation” in the ring waveguide. Since the effect of notches can be described using the well understood perturbation theory, analysis of the effect of WSR using notches can be performed using eigenmode solvers. Experiments depict that our abstraction is quite accurate to full-scale FDTD simulations, but is orders of magnitude faster.